Dual-sPLS: a family of Dual Sparse Partial Least Squares regressions for feature selection and prediction with tunable sparsity; evaluation on simulated and near-infrared data

Relating a set of variables X to a response y is crucial in chemometrics. A quantitative prediction objective can be enriched by qualitative data interpretation, for instance by locating the most influential features. When high-dimensional problems arise, dimension reduction techniques can be used. Most notable are projections (e.g. Partial Least Squares or PLS ) or variable selections (e.g. lasso). Sparse partial least squares combine both strategies, by blending variable selection into PLS. The variant presented in this paper, Dual-sPLS, generalizes the classical PLS1 algorithm. It provides balance between accurate prediction and efficient interpretation. It is based on penalizations inspired by classical regression methods (lasso, group lasso, least squares, ridge) and uses the dual norm notion. The resulting sparsity is enforced by an intuitive shrinking ratio parameter. Dual-sPLS favorably compares to similar regression methods, on simulated and real chemical data. Code is provided as an open-source package in R: \url{https://CRAN.R-project.org/package=dual.spls}.